Castillo, 25, signed for Red Star Belgrade from El Nacional last summer on a two-year deal.
"At the moment I am in Austria with my current team doing pre-season work, but I have heard that Juventus are interested in me," he said.
"Truthfully, the news took me by surprise, but I am very happy about it.
"Some of my team-mates have told me that they heard the Italian media saying I will be wearing the Juventus shirt very soon, but I cannot confirm that until someone tells me something officially."
Sources in Ecuador also claim that Juventus watched Castillo in action at the recent Copa America in Venezuela, adding that they expect him to sign a contract on Wednesday.